find interval of Legendre and 2 other estimated primes from two entries

Type:

Patch

Version:

8.6

Submitter:

anonymous

Created on:

2018-07-31 00:57:43

Subsystem:

math :: special

Assigned To:

arjenmarkus

Priority:

5 Medium

Severity:

Cosmetic

Status:

Closed

Last Modified:

2019-04-24 19:02:32

Resolution:

Accepted

Closed By:

arjenmarkus

Closed on:

2019-04-24 19:02:32

Description:

possibly, difference over interval using NumberPrimesLegendreModified (related previous ticket cd42b3ddf8,2017-05-28 )
would be useful to some. two numbers entered, limit1 and limit2 and difference returned. both limits must be greater than one. find interval of est. primes from two entries on positive number line. Inclusive, interval differences for numberPrimesGauss, numberPrimesLegendre, NumberPrimesLegendreModified might be useful.
##
### differenceNumberPrimesLegendreModified --
# Return the approximate difference number of primes
# between a lower and higher limit as given values
# for approximate number of primes based on the
# modified formula by Legendre
#
# Arguments:
# limit1 The lower limit for the interval, largest prime to be included in the l.limit
# limit2 The upper limit for the interval, largest prime to be included in the u.mlimit
#
# Returns:
# Approximate difference number of primes
#
proc ::math::numtheory::differenceNumberPrimesLegendreModified {limit1 limit2} {
if { $limit1 <= 1 } {
return -code error "The lower limit must be larger than 1"
}
if { $limit2 <= 1 } {
return -code error "The upper limit must be larger than 1"
}
set aa [::math::numtheory::numberPrimesLegendreModified [expr ($limit1)]]
set bb [::math::numtheory::numberPrimesLegendreModified [expr ($limit2)]]
expr ( $bb-$aa)
}
#######
statements invoking difference
puts " [ ::math::numtheory::differenceNumberPrimesLegendreModified 100 200 ] "
#puts " [ ::math::numtheory::differenceNumberPrimesLegendreModified 100 0 ] " invokes error.

User Comments:

arjenmarkus added on 2019-04-24 19:02:02:

I was a trifle hasty with my conclusion. The procedures I was looking for are contained in the file primes.tcl.
Added the above convenience procedure and updated the tests and the manual.
(Note to self: still a bunch of tests to be added!)

arjenmarkus added on 2019-04-18 19:05:54:

Hm, it turns out that the file numtheory.tcl contains only a small part of the original package. I will need to examine this more closely. This requires a new ticket, as I cannot currently apply this rightaway.

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